7' Homework Instr ions: Complete the following problems; Submit responsm as a single PDF le in Black- board For full credit, solutions must be justied and include supporting work when appropriate. 1. A multiple choice test contains 10 questions. There are four possible answers for each question. (a) How many ways can a student complete the test if every question must be answered? (b) How many ways can a student complete the test if questions can be left unanswered? 2. A codeword is either a sequence of three letters followed by two digits or two letters followed by three digits. Assume letters are not camesensitive. (a) How many dierent codewords are possible if repeats are allowed? (b) How many djerent codewords are possible if repeats are not allowed? Hint Letters refer to the standard 264etter alphabet; digits are elements of {0, 1, 2, 3, 4, 5, 6, T, B, 9}, 3. A team of size 5 'E selected Erom a group of 8 programmers and 12 cyber security analysts. (a) How many dierent team are possible? (b) How many teams are possible ifexaetly 2 programmers must he on the committee? (c) How many teams are possible if the programmers must outnumber the cyber security analysts on the team? 4. Recall, a bit string is a sequence of 0's and 1's. (4;) How many bit strings of length eight has exactly three D's? (b) How many bit strings of length eight have at most two D's? (c) How many bit strings of length eight start and end with 1's? 5. Suppose that all employees at a certain business use Mac, Windows, or Linux as their op- erating system. Assume that there are 11 Mac users, 13 Windows users, and 3 Linux users at the business. Additionally, ve employees use both Mac and Windows, two use both Mac and Linux, two use both Windows and Linux, and one uses all three How many employees does; the business have